There has been a growing interest in investigating genetic architecture of time-varying functional traits such as blood pressure, cholesterol levels or growth rate. Few of the methods proposed in the literature, however, are sufficiently general to apply to complicated situations in a computationally feasible fashion. The goal of this research is to develop general and more powerful statistical methods to map functional quantitative genetic traits. More specifically, in the first step we propose a non-parametric permutation test for overall genetic effect of functional traits by examining familial aggregation. When there is evidence for genetic contribution, the natural second step is to estimate this overall polygenic effect. We then develop methods based on mixed effects models for estimation and use functional principal components analysis to summarize the major temporal variation of the polygenic effect. When the overall genetic effect is reasonably strong, research interest lies in locating influential genes on the genome. In the third step, we propose general functional variance components models to test and estimate quantitative trait locus (QTL) genetic effects using marker genotype data in a genome-wide linkage study. Current ad-hoc methods either uses averages of repeated measurements in a univariate analysis or specifies a parametric form of time- dependent genetic effects in a longitudinal analysis. We propose a family of basis systems to capture genetic effects and estimate age-specific QTL heritability. The flexibility of such basis systems allow for identification of temporal trends of any shape. Within this functional mapping framework, we can answer research questions such as when is a QTL effect expressed to affect a trait, how does gene affect rate of change of traits and so on. Lastly, we propose to investigate our methods using Genetic Analysis Workshop (GAW) 13 simulated data, apply them to the Framingham Heart Study data, and implement them in a software package. Framingham Heart Study is a large prospective study of cardiovascular disease which aims to investigate risk factors and genetic architecture of this disease. The GAW13 simulation data was generated closely based on the Framingham Study, which provides a realistic and valuable resource for methods evaluation and comparison. An application of the developed methods to Framingham data may enhance our understanding of the genetic architecture of cardiovascular disease related traits. The developed software will be made publicly available to all investigators free of charge. PUBLIC HEALTH RELEVANCE: Dissecting genetic determinants of complex time-varying functional traits such as blood pressure, cholesterol levels or growth rate has been one of the most daunting tasks in genetic studies due to complicated nature of their etiology. This project develops new statistical methods to map genetic variants predisposing complex functional traits and applies methods to the Framingham Heart Study data. The study will offer general and more powerful analysis methods for mapping functional quantitative genetic trait and to answer research questions such as when is a gene expressed to affect a trait, how long does genetic effect last, and how does gene affect rate of change of traits.